Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 10 - Section 10.5 - The Binomial Theorum - Exercise Set - Page 1093: 80


False. There are no nonzero values of $a$ and $b$ such that$$(a+b)^4=a^4+b^4.$$

Work Step by Step

Please note that if at least one of $a$ or $b$ is zero, say $b=0$, then the identity holds true: $$(a+0)^4=a^4=a^4+0^4.$$ However, for nonzero values of $a$ and $b$, the identity does not hold because the binomial expansion of $(a+b)^4$ has the terms $a^{4-r}b^r$, $r=1, 2, 3$, which are nonzero.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.